With a fuel injection nozzle known from German Published, Non-Examined Patent Application DE-OS 33 00 953, for example, the relatively short injection holes, embodied as blind bores, extend at a low conical angle in the closing head and terminate at the circumference of a cylindrical segment of the closing head that is enclosed by the nozzle body. Supply conduits, starting from a conical segment disposed in front of the cylindrical segment and extending at a steep angle in the closing head, terminate in the injection holes at right angles. Also, because the cross-section of a supply conduit is only slightly larger than that of the injection hole, a severe deflection of the flow occurs at the transition of the supply conduit into the injection hole, and a non-homogenous velocity distribution in the flow in the injection hole and also in its discharge opening occurs due to the varying influx and deflection conditions. An axial component of the supply conduit is also superimposed onto the flow in the injection hole; this component remains uncompensated in the short length of the injection hole, so that the fuel stream exiting the injection hole is diverted in the orientation of the injection hole in the direction of the axial component.